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We demonstrate time-of-flight measurements for an ultracold levitated nanoparticle and reveal its velocity for the translational motion brought to the quantum ground state. We discover that the velocity distributions obtained with repeated release-and-recapture measurements are significantly broadened via librational motions of the nanoparticle. Under feedback cooling on all the librational motions, we recover the velocity distributions in reasonable agreement with an expectation from the occupation number, with approximately twice the width of the quantum limit. The strong impact of librational motions on the translational motions is understood as a result of the deviation between the libration center and the center of mass, induced by the asymmetry of the nanoparticle. Our results elucidate the importance of the control over librational motions and establish the basis for exploring quantum mechanical properties of levitated nanoparticles in terms of their velocity., Comment: 8 pages, 7 files

We demonstrate feedback cooling of all the angular motions of a near-spherical neutral nanoparticle with all the translational motions feedback-cooled to near the ground state. The occupation numbers of the three translational motions are $6 \pm 1$, $6 \pm 1$, and $0.69 \pm 0.18$. A tight, anisotropic optical confinement allows us to clearly observe three angular oscillations and to identify the ratio of two radii to the longest radius with a precision of $\unit[0.09]{\%}$. We develop a thermometry for three angular oscillations and realize feedback cooling of them to temperatures of lower than $\unit[0.03]{K}$ by electrically controlling the electric dipole moment of the nanoparticle. Our work not only paves the way to precisely characterize trapped nanoparticles, but also forms the basis of utilizing them for acceleration sensing and for exploring quantum mechanical behaviors with both their translational and rotational degrees of freedom., Comment: 10 pages, 11 figures, 1 table

We report on direct feedback cooling of single nanoparticles in an optical lattice to near their motional ground state. We find that the laser phase noise triggers severe heating of nanoparticles' motion along the optical lattice. When the laser phase noise is decreased by orders of magnitude, the heating rate is reduced and accordingly the occupation number is lowered to about three. We establish a model directly connecting the heating rate and the measured laser phase noise and elucidates that the occupation number under the lowest laser phase noise in our system is limited only by photon recoil heating. Our results show that the reduction of the laser phase noise near the oscillation frequency of nanoparticles is crucial for bringing them near the ground state and pave the way to sensitive accelerometers and quantum mechanical experiments with ultracold nanoparticles in an optical lattice., Comment: 7 pages, 5 figures

We demonstrate feedback cooling of the center-of-mass motion of single charged nanoparticles to millikelvin temperatures in three dimensions via applying oscillating electric fields synchronized to their optically observed motion. The observed motional temperatures at weak feedback agree with a simple model and allow us to estimate the charge number of trapped nanoparticles. The agreement between our model and experiments is confirmed by independent measurements of the charge numbers based on a shift in the oscillation frequency induced by a constant electric field. The demonstrated temperature of below 10 mK at $4 \times 10^{-3}$ Pa is lower than that with the conventional optical cooling approach at this pressure by one to two orders of magnitude. Our results form the basis of manipulating cold charged nanoparticles and paves the way to quantum mechanical studies with trapped nanoparticles near their ground state., Comment: 6 pages, 5 figures

We show that at low pressures the spectral widths of the power spectra of laser-trapped particles are nearly independent from pressures and, due to the nonlinearities of the trap, reflect the thermal distribution of particles. In the experiments with nanoparticles trapped in an optical lattice, we identify two distinct features of the widths. First, the widths along an optical lattice are much broader than those in the other directions. Second, the spectral widths are narrower for larger nanoparticles. We develop a theory of thermal broadening and show that the spectral widths normalized by the frequencies of the center-of-mass motion directly reveal the ratio of the thermal energy to the trap depth. The presented model provides a good understanding of the observed features. Our model holds also for smaller particles such as atoms and molecules and can be readily extended to the general case with a single-beam optical trap., Comment: 9 pages, 9 figures

The Hubbard model underlies our understanding of strongly correlated materials. While its standard form only comprises interaction between particles at the same lattice site, its extension to encompass long-range interaction, which activates terms acting between different sites, is predicted to profoundly alter the quantum behavior of the system. We realize the extended Bose-Hubbard model for an ultracold gas of strongly magnetic erbium atoms in a three-dimensional optical lattice. Controlling the orientation of the atomic dipoles, we reveal the anisotropic character of the onsite interaction and hopping dynamics, and their influence on the superfluid-to-Mott insulator quantum phase transition. Moreover, we observe nearest-neighbor interaction, which is a genuine consequence of the long-range nature of dipolar interactions. Our results lay the groundwork for future studies of novel exotic many-body quantum phases., Comment: 11 pages, 7 figures

We show that for ultracold magnetic lanthanide atoms chaotic scattering emerges due to a combination of anisotropic interaction potentials and Zeeman coupling under an external magnetic field. This scattering is studied in a collaborative experimental and theoretical effort for both dysprosium and erbium. We present extensive atom-loss measurements of their dense magnetic Feshbach resonance spectra, analyze their statistical properties, and compare to predictions from a random-matrix-theory inspired model. Furthermore, theoretical coupled-channels simulations of the anisotropic molecular Hamiltonian at zero magnetic field show that weakly-bound, near threshold diatomic levels form overlapping, uncoupled chaotic series that when combined are randomly distributed. The Zeeman interaction shifts and couples these levels, leading to a Feshbach spectrum of zero-energy bound states with nearest-neighbor spacings that changes from randomly to chaotically distributed for increasing magnetic field. Finally, we show that the extreme temperature sensitivity of a small, but sizeable fraction of the resonances in the Dy and Er atom-loss spectra is due to resonant non-zero partial-wave collisions. Our threshold analysis for these resonances indicates a large collision-energy dependence of the three-body recombination rate.

In a combined experimental and theoretical effort, we demonstrate a novel type of dipolar system made of ultracold bosonic dipolar molecules with large magnetic dipole moments. Our dipolar molecules are formed in weakly bound Feshbach molecular states from a sample of strongly magnetic bosonic erbium atoms. We show that the ultracold magnetic molecules can carry very large dipole moments and we demonstrate how to create and characterize them, and how to change their orientation. Finally, we confirm that the relaxation rates of molecules in a quasi-two dimensional geometry can be reduced by using the anisotropy of the dipole-dipole interaction and that this reduction follows a universal dipolar behavior., Comment: 8 pages, 5 figures, including supplemental material

The deformation of a Fermi surface is a fundamental phenomenon leading to a plethora of exotic quantum phases. Understanding these phases, which play crucial roles in a wealth of systems, is a major challenge in atomic and condensed-matter physics. Here, we report on the observation of a Fermi surface deformation in a degenerate dipolar Fermi gas of erbium atoms. The deformation is caused by the interplay between strong magnetic dipole-dipole interaction and the Pauli exclusion principle. We demonstrate the many-body nature of the effect and its tunability with the Fermi energy. Our observation provides basis for future studies on anisotropic many-body phenomena in normal and superfluid phases., Comment: 6 pages, 5 figures

We report on the observation of a large anisotropy in the rethermalization dynamics of an ultracold dipolar Fermi gas driven out of equilibrium. Our system consists of an ultracold sample of strongly magnetic $^{167}$Er fermions, spin-polarized in the lowest Zeeman sublevel. In this system, elastic collisions arise purely from universal dipolar scattering. Based on cross-dimensional rethermalization experiments, we observe a strong anisotropy of the scattering, which manifests itself in a large angular dependence of the thermal relaxation dynamics. Our result is in very good agreement with recent theoretical predictions. Furthermore, we measure the rethermalization rate as a function of temperature for different angles and find that the suppression of collisions by Pauli blocking is not influenced by the dipole orientation., Comment: 5 pages, 4 figures

We propose and experimentally investigate a scheme for narrow-line cooling of KRb molecules in the rovibrational ground state. We show that the spin-forbidden $\mathrm{X^1\Sigma^+} \rightarrow \mathrm{b^3\Pi_{0^+}}$ transition of KRb is ideal for realizing narrow-line laser cooling of molecules because it has highly diagonal Franck-Condon factors and narrow linewidth. In order to confirm the prediction, we performed the optical and microwave spectroscopy of ultracold $^{41}$K$^{87}$Rb molecules, and determined the linewidth ($2\pi\times$ 4.9(4) kHz) and Franck-Condon factors for the $\mathrm{X^1\Sigma^+} (v''=0) \rightarrow \mathrm{b^3\Pi_{0^+}} (v'=0)$ transition (0.9474(1)). This result opens the door towards all-optical production of polar molecules at sub-microkelvin temperatures., Comment: 4 pages, 5 figures

We report on the creation of a degenerate dipolar Fermi gas of erbium atoms. We force evaporative cooling in a fully spin-polarized sample down to temperatures as low as 0.2 times the Fermi temperature. The strong magnetic dipole-dipole interaction enables elastic collisions between identical fermions even in the zero-energy limit. The measured elastic scattering cross section agrees well with the predictions from dipolar scattering theory, which follow a universal scaling law depending only on the dipole moment and on the atomic mass. Our approach to quantum degeneracy proceeds with very high cooling efficiency and provides large atomic densities, and it may be extended to various dipolar systems., Comment: 5 pages, 4 figures

We report on the achievement of Bose-Einstein condensation of erbium atoms and on the observation of magnetic Feshbach resonances at low magnetic field. By means of evaporative cooling in an optical dipole trap, we produce pure condensates of $^{168}$Er, containing up to $7 \times 10^{4}$ atoms. Feshbach spectroscopy reveals an extraordinary rich loss spectrum with six loss resonances already in a narrow magnetic-field range up to 3 G. Finally, we demonstrate the application of a low-field Feshbach resonance to produce a tunable dipolar Bose-Einstein condensate and we observe its characteristic d-wave collapse., Comment: 4 pages, 3 figures

We report on the experimental realization of a robust and efficient magneto-optical trap for erbium atoms, based on a narrow cooling transition at 583nm. We observe up to $N=2 \times 10^{8}$ atoms at a temperature of about $T=15 \mu K$. This simple scheme provides better starting conditions for direct loading of dipole traps as compared to approaches based on the strong cooling transition alone, or on a combination of a strong and a narrow kHz transition. Our results on Er point to a general, simple and efficient approach to laser cool samples of other lanthanide atoms (Ho, Dy, and Tm) for the production of quantum-degenerate samples.

We investigated transition strengths from ultracold weakly bound 41K87Rb molecules produced via the photoassociation of laser-cooled atoms. An accurate potential energy curve of the excited state (3)1Sigma+ was constructed by carrying out direct potential fit analysis of rotational spectra obtained via depletion spectroscopy. Vibrational energies and rotational constants extracted from the depletion spectra of v'=41-50 levels were combined with the results of the previous spectroscopic study, and they were used for modifying an ab initio potential. An accuracy of 0.14% in vibrational level spacing and 0.3% in rotational constants was sufficient to predict the large observed variation in transition strengths among the vibrational levels. Our results show that transition strengths from weakly bound molecules are a good measure of the accuracy of an excited state potential., Comment: 7 pages, 7 figures

We report on the direct conversion of laser-cooled 41K and 87Rb atoms into ultracold 41K87Rb molecules in the rovibrational ground state via photoassociation followed by stimulated Raman adiabatic passage. High-resolution spectroscopy based on the coherent transfer revealed the hyperfine structure of weakly bound molecules in an unexplored region. Our results show that a rovibrationally pure sample of ultracold ground-state molecules is achieved via the all-optical association of laser-cooled atoms, opening possibilities to coherently manipulate a wide variety of molecules., Comment: 4 pages, 4 figures

We have investigated the collisional properties of 41K atoms at ultracold temperature. To show the possibility to use 41K as a coolant, a Bose-Einstein condensate of 41K atoms in the stretched state (F=2, m_F=2) was created for the first time by direct evaporation in a magnetic trap. An upper bound of three body loss coefficient for atoms in the condensate was determined to be 4(2) 10^{-29} cm -6 s-1. A Feshbach resonance in the F=1, m_F=-1 state was observed at 51.42(5) G, which is in good agreement with theoretical prediction., Comment: 4 pages, 4 figures